Effect Of Loading Path Research Articles

Effect of loading sequence on the ultra-low-cycle fatigue performance of all-steel BRBs

Buckling-restrained braces (BRBs) are intended to protect the primary structure of buildings by absorbing most earthquake input energy through the plastic deformation of the steel cores. The ultra-low-cycle fatigue performance of BRBs is crucial for their seismic performance as energy dissipators. Despite the plenty of research on the ultra-low-cycle fatigue behavior of steel members, it remains susceptible if arbitrary loading paths have a major effect on the ultra-low-cycle fatigue life or cumulative plastic deformation (CPD) capacity of BRBs. This paper introduces an experimental campaign of nine supposedly identical BRB specimens subjected to three different loading protocols of similar average strain amplitudes. For each loading protocol, the test was repeated for three times to account for possible uncertainty. The results show that the effect of loading protocol is trivial given the similar average strain amplitudes throughout the loading. The Miner's assumption that the loading sequence has no effect on the fatigue life of BRBs is supported by the test results, however, the proper choice of the Coffin-Masson model's parameters is crucial. The skeleton ratio, which is derived from decomposing the hysteresis curve into a skeleton part and a Bauschinger part and has been used to account for the loading path effects, is shown to be insensitive to varied loading protocols by the test results.

A Multipath Process-Based Inherent Strain Method for Prediction of Deformation of Hull Plate for Integrated Heating and Mechanical Rolling Forming Process

Integrated heating and mechanical rolling forming (IHMRF) has recently been introduced for manufacturing complex curvature hull plates. It fabricates the target curved plate by sequential loading along the multipath. Accurate and efficient prediction of the deformation of the plate is the basis for developing the process planning and ensuring the quality of the forming. The inherent-strain method is ideal for this purpose, but its prediction accuracy needs to be improved. This paper proposes a multipath process-based inherent-strain method (MPISM), which considers the effect of the sequential loading process of the multipath on plate deformation. First, the effect of loading paths near the plate edge was investigated, which in turn clarified the rationale for obtaining the inherent strain only in the plate center. Secondly, a strain correction strategy was established by analyzing the variation pattern of the inherent strain caused by the crossing or proximity of the previous path and the subsequent path. This allowed the effects of the loading process to be taken into account in the elastic analysis. Based on the plate-and-shell theory, the idea of an equivalent inherent strain distribution is also presented. This makes the loading of inherent strains more accurate in the elastic finite-element model. MPISM predictions and experimental results show good agreement. Compared with the thermo-elastic–plastic finite element method, the MPISM substantially improves efficiency while maintaining accuracy. Compared with the original inherent-strain method, the MPISM is more accurate in terms of deformation magnitude prediction.

Failure mechanism of hot dry rock under the coupling effect of thermal cycling and direct shear loading path

Inducing shear failure in reservoir rocks is a critical strategy for enhancing hot dry rock resource exploitation, as it promotes the development of an extensive fracture network. In this study, granite was subjected to direct shear tests under three distinct temperatures and five thermal cycling treatments. Utilizing acoustic emission (AE) and digital image correlation (DIC) techniques, the shear failure traits and the evolutionary patterns of cracks in granite under diverse thermal cycling treatments were probed. Experimental results reveal that the direct shear strength of granite initially decreases, subsequently rebounds with increasing thermal cycles, and exhibits a steady decrease with temperature increase. Effects of thermal shock provoke a surge in AE counts and energy during the initial half of the shearing process, steering the failure mode of the samples from brittle to plastic. Furthermore, the macro crack morphology changes from a singular shear crack to a pair of parallel shear cracks, becoming intricately complex at elevated temperatures (600 °C). Additionally, the initiation of the main shear crack in granite consistently manifests a mixed tensile-shear failure, with the proportion of shear action displaying a positive correlation with temperature. In contrast, the proximal secondary cracks are purely tension-initiated. Finally, a competitive mechanism between rock strengthening and weakening induced by thermal cycles treatment was proposed to explain the remarkable rebound in direct shear strength following thermal cycling treatment. The current work provides insights for the mechanism of shear failure in rocks under different thermal cycling conditions in geothermal reservoir stimulation.

Mechanical response and energy evolution of interbedded shales subjected to multilevel constant/increasing-amplitude cyclic loading

This study aims to investigate the effects of fatigue loading paths and interbed structure on the mechanical properties and energy evolution characteristics of shales. In the experiments, shale specimens with five types bedded angles (0°, 30°, 45°, 60°, 90°) were prepared, and multilevel constant-amplitude fatigue loading test (MCFT) and multilevel variable-amplitude fatigue loading test (MVFT) were performed. Results indicated that shale's fatigue behaviors were highly affected by the bedding plane angles and the cyclic loading paths. Specifically, with the increasing of bedding angle, the peak strength, total dissipated energy, and total input energy of the shales showed a "U" trend, the ultimate macro-damage mode changed from mixed tension-shear failure to failure along the bedding planes, and the damping ratio firstly increased and then decreased. Test schemes of stepwise increase of the lower stress limit or keeping it constant were the differences between MCFT and MVFT, which significantly influenced the evolution of irreversible deformation of shales. Compared to MVFT, the shale in MCFT displayed reduction in peak strength in the range of 4.3% to 23.9%, greater and more drastic variations in elastic modulus and damping ratios, dissipative energy and elastic strain energy were relatively low by an order of magnitude.

Experimental investigation on mechanical behavior of silane‐modified polyurethane sealant under biaxial cyclic loading

AbstractThe biaxial tension–tension cyclic loading experiments were conducted on the cruciform specimens prepared using a silane‐modified polyurethane sealant to investigate their mechanical behavior. The finite element method was employed to validate the mechanical behavior of cruciform specimens under the biaxial cyclic loading conditions. It is shown that the highest stress concentration is in the central region of the cruciform specimens, indicating that the shape design of the specimen is suitable for the biaxial tension–tension cyclic tests. Additionally, the effects of loading path, mean stress, and stress amplitude on ratcheting strain and dissipated energy were analyzed through the experimental data. The experimental results demonstrated that the loading path had an influence on the mechanical behavior of the cruciform specimen. The additional ratcheting strain caused by the non‐proportional loading path was found to be loading path dependent of the adhesive. Moreover, the mean stress and stress amplitude greatly affected the strain response curves of the specimen under biaxial cyclic loading. The ratcheting strain and dissipated energy increased with increasing mean stress and stress amplitude; nevertheless, stress amplitude had more influence on the mechanical behavior than the mean stress.

Stick-slip in a stack: How slip dissonance reveals aging

We perform physical and numerical experiments to study the stick-slip response of a stack of slabs in contact through dry frictional interfaces driven in quasistatic shear. The ratio between the drive's stiffness and the slab's shear stiffness controls the presence or absence of slip synchronization. A sufficiently high stiffness ratio leads to synchronization, comprising periodic slip events in which all interfaces slip simultaneously. A lower stiffness ratio leads to asynchronous slips and, experimentally, to the stick-slip amplitude becoming broadly distributed as the number of layers in the stack increases. We interpret this broadening in light of the combined effect of complex loading paths, due to the asynchronous slips, and interface aging. Consequently, the aging rate of the interfaces can be readily extracted from the stick-slip cycles, and it is found to be of the same order of magnitude as existing experimental results on a similar material. Finally, we discuss the emergence of slow slips and an increase in aging-rate variations when more slabs are added to the stack. Published by the American Physical Society 2024

Suppressing wrinkles in thin-walled dome parts: A novel deep drawing method with active stress control

The occurrence of wrinkling defects in deep drawing thin-walled dome parts is primarily attributed to circumferential compressive stress. With a decrease in the thickness-to-diameter ratio, preventing wrinkling becomes increasingly challenging during the forming process. This study proposes a novel deep drawing method that effectively suppresses wrinkles in thin-walled dome parts through the utilization of a local reverse bulging tool for active stress control. An analytical model is developed to describe this novel deep drawing method, enabling analysis of the radius variations in the reverse bulging area and the corresponding reverse bulging force. Numerical simulations are carried out to investigate the effect of the reverse bulging loading path on the stress-strain distribution. Furthermore, experimental trials are performed under various loading conditions to explore the impact of loading paths on forming defects and thickness distributions of the formed parts. The findings indicate that the radius of rigid tools and the reverse bulging force play pivotal roles in achieving the desired reverse bulging effect. As the punch stroke increases, the radius of the reverse bulging area decreases, while the reverse bulging force exhibits a pattern of initial increase followed by a subsequent decrease. By employing an appropriate reverse bulging loading path, the circumferential stress at the reverse bulging area transitions from compressive stress to tensile, effectively suppressing the occurrence of wrinkles. This research provides valuable experimental guidance for implementing the novel deep drawing process for dome parts.

Experimental study on effects of cyclic loading paths on cracking behavior and fracture characteristics of granite

To investigate the impact of cyclic loading paths on the Mode I fracture characteristics of granite, a series of fracture tests were conducted on semi-circular bend (SCB) specimens using acoustic emission (AE), digital image correlation (DIC) and 3D scanning. The tests included monotonic loading, variable amplitude (VA) cyclic loading, and tiered constant amplitude (TCA) cyclic loading. The results demonstrated that VA cyclic loading leads to an average enhancement of 5.6% in fracture toughness, whereas TCA cyclic loading results in an average reduction of 3.7% in fracture toughness. During cyclic loading and unloading, the TCA loading path exhibits a higher rate of cumulative plastic deformation growth and greater magnitude cumulative plastic deformation compared to the VA loading path. Additionally, detailed observations from 3D scanning revealed that under cyclic loading, the fracture trajectories and surface morphology exhibit more tortuosity and roughness compared to monotonic loading, particularly in the case of TCA cyclic loading. Furthermore, according to the AE and DIC analysis, the proportion of microcrack initiation and stable propagation stage, cumulative AE counts and fracture process zone (FPZ) size generated under VA cyclic loading are greater than those generated under TCA cyclic loading, displaying a consistent variation pattern with fracture toughness. The changes of fracture properties can be attributed to a competition between the compaction-induced hardening effect and the cracking-induced damage effect. A higher cyclic upper limit and incomplete unloading are more likely to accelerate the growth of the irreversible crack damage and rapid crack extension, resulting in weakened rock fracture properties. These findings provide important references for rock instability control in underground rock engineering.

Coexistence of five domains at single propagating interface in single-crystal Ni[sbnd]Mn[sbnd]Ga shape memory alloy

Coexistence of both austenite and martensite during phase transformation is a common feature of all Shape Memory Alloys (SMAs). The martensite has different variants featuring characteristic deformations rotationally linked to each other due to the symmetries of the austenite parent phase, and the martensite variants can form twins with different mean characteristic deformations. Multiple-domain microstructures (consisting of austenite, martensite twins and individual martensite variants) evolve collectively within an SMA sample during the phase transformation, contributing thus to the material's macroscopic response (e.g., its global deformation). Particularly, the multiple domains can exist at the diffuse austenite-martensite interface nucleating and propagating in a single crystal in certain conditions. This implies an energy barrier for this interfacial structure, influencing the interface kinetics and the driving force (energy dissipation) of the phase transformation. In this paper, we report an experimentally observed interface consisting of five domains (austenite, one martensite variant and three twins) in a Ni–Mn–Ga single-crystal initially consisting of one martensite variant and subjected to a uniaxial thermal gradient. The compatibility analysis (performed from the characteristic strains of the three martensite variants having approximately a tetragonal symmetry) reveals that the five-domain interface is not a perfectly compatible pattern like the basic habit plane (consisting of only one twin compatible with austenite). However, its level of non-compatibility is similar to that of the quite common X-interface (four-domain coexistence) which is observed in many SMAs. Further, the significant effects of the thermal loading path and the material initial state (the initial martensite variant) on the domain pattern formation are demonstrated and analyzed. The experimental observation and the theoretical analysis of the domain patterns can provide hints to better understand diffuse interface kinetics and phase transformation hysteresis.

Effect of biaxial cyclic loading path on the mechanical and microstructure properties of articular cartilage

Cyclic loading stimulation has the potential to change both the mechanical properties and microstructure of cartilage, subsequently damaging the articular cartilage and contributing to joint osteoarthritis. This study focuses on investigating the behavior of knee articular cartilage under biaxial cyclic loading and analyzing the associated microstructural changes at the ultrastructural level. We studied the in-plane biaxial cyclic loading behavior of cartilage with a particular emphasis on understanding the effects of loading paths, taking into consideration the complex loading conditions encountered during daily activities. The experimental results reveal a clear influence of the constraints in the Y-direction (orthogonal direction) on the strain evolution in the X-direction. Furthermore, the variation in orthogonal stress corresponding to the loading path significantly impacts the biaxial mean strain of the test sample. To be specific, the uniaxial path, characterized by no constraints in the Y-direction, demonstrates the highest mean strain of 25.08 ± 0.88% in the X-direction, while the proportional path exhibits the lowest mean strain (10.77 ± 0.49%) in the X-direction due to the Y-direction's largest stress constraint. We explored the effects of stress amplitude and peak stress holding time on mean strain under a square path. Our observations indicate that the mean strain of cartilage increases with the higher stress amplitude or the longer peak stress holding time. Additionally, we analyzed the collagen fibril networks before and after biaxial cyclic loading to reveal the intrinsic deformation mechanism. The rearrangement of collagen fibril networks is closely associated with the stress state of cartilage, where higher stress levels lead to more severe fibril damage.

Effect of loading paths on hydroforming ability of stepped hollow shaft components from double layer pipes

The step hollow shaft components are composed of two layers of different materials, they are formed using tube hydroforming process due to its high strength and rigidity, low weight and flexible profiles, compared to traditional casting, welding, and forming methods. These products are effectively used in industries such as the automotive, shipbuilding, aerospace and defense, and oil and gas sectors. The success of various double layer pipe hydroforming process depends on several factors, with the most important being the internal pressure path and axial loading path. This paper presents research on the effect of input loading paths on the hydroforming ability of a different two-layer metal structure - an outer layer of SUS304 stainless steel and an inner layer of CDA110 copper - using 3D numerical simulations on Abaqus/CAE software. Output criteria were used to evaluate the forming ability of the formed components, including Von Mises stress, Plastic strain component (PEmax), wall thinning, and pipe profile, based on which the input loading paths were combined during the forming process. These output criteria allow for more accurate predictions of material behavior during the hydroforming process, as well as deformation and stress distribution. This can support the design process, improve product quality, reduce errors, and increase production efficiency. The research results can be applied as a basis for optimizing load paths for the next experimental step in the near future, for undergraduate and graduate training, as well as allowing designers and engineers to optimize the process of hydroforming of different 2-layer tubes, reducing costs, improving accuracy, flexible design, minimizing risks, and increasing efficiency

Improving Material Formability and Tribological Conditions through Dual-Pressure Tube Hydroforming

Dual-pressure tube hydroforming (THF) is a tube-forming process that involves applying fluid pressure to a tube’s inner and outer surfaces to achieve deformation. This study investigates the effect of dual-pressure loading paths on material formability and tribological conditions. Specifically, pear-shaped and triangular cross-sectional parts were formed using dual-pressure modes where fluid pressure on the inside of the tubular blank was alternated with pressure on the outside surface of the tubular blank, causing the tube to expand/stretch and contract. During expansion, the tube conformed to the die’s cavity, while during contraction, the contact area between the die and the workpiece reduced, leading to decreased friction stress at the tube–die interface. Additionally, the reversal of pressure loadings caused the tubular blank to buckle, altering the stress state and potentially increasing local shear stress, improving material formability. Dual-pressure THF has demonstrated that the pressure loading paths chosen can substantially influence material formability. Comparing the geometries of parts formed by dual-pressure THF and conventional THF shows a significant increase in the protrusion height of both the pear-shaped and triangular specimens using dual-pressure THF.

Cyclic behavior and ultimate bearing capacity of circular concrete-filled double skin steel tube members subjected to combined compression and torsion

This paper presents a pseudo-static test investigation and finite element analysis on the behavior of circular concrete-filled double skin steel tube (CFDST) members under axial compression and torsion. The hollow ratio (χ) and axial compression ratio (n) are considered in the test study. The ductility, hysteretic behavior, failure modes, and compression–torsion correlation of circular CFDST members are discussed. The comparison results show that the validated finite element model is capable to capture the behavior of circular CFDST members under compression and torsion. The effect of loading paths and various parameters on the compression–torsion correlation of circular CFDST members are analyzed. Parametric analyses are carried out to investigate the effect of key parameters, such as material properties, nominal steel ratio, the wall thickness of inner steel tube, and hollow ratio on the compression–torsion correlation of circular CFDST members. It can be seen that the circular CFDST members under compression and torsion possess good load-bearing capacity, energy dissipation, and ductility properties. The loading paths, yield strength of inner and outer steel tubes, nominal steel ratio, and the wall thickness of inner steel tubes have little effect on the compression–torsion correlation of the composite members. When the axial compression ratio is less than 0.2, the axial compression load can slightly improve the torque capacity of circular CFDST members. Finally, the compression–torsion correlation equation of these members was proposed by regression analysis, and design formulas with good accuracy for predicting the torque capacity of circular CFDST members under compression and torsion were proposed.

Cyclic Behavior of Rectangular Bridge Piers Subjected to the Coupling Effects of Chloride Corrosion and Bidirectional Loading

The degradation of seismic performance for RC bridge piers induced by chloride corrosion has previously been studied by treating the earthquake as a unilateral cyclic loading. Such studies do not consider the true response of the pier under the joint effect of corrosion damage and real multi-dimensional earthquake action. Thus, in the present study, the cyclic behavior of rectangular bridge piers subjected to the coupling effects of chloride corrosion and bidirectional loading was numerically investigated. First, the corrosion-induced deterioration of material mechanical properties is introduced. Second, the numerical model of two corroded piers is built and validated with the test results in the literature. Then, the time-dependent biaxial seismic performance of a rectangular bridge pier under the circular-shaped (CS) biaxial displacement pattern, square-shaped (SS) biaxial displacement pattern, uniaxial displacement in the X-direction (UX) pattern, and uniaxial displacement in the Y-direction (UY) pattern is analyzed using the validated model. The simulation results conclude that the trajectory of biaxial loading paths and corrosion levels significantly influence the peak force, deformation capacity, and dissipated energy of the piers. The biaxial loading path effect for the corrosive pier includes two stages with different biaxial force trajectory characteristics. Compared with the uncorroded pier, the corrosion level of 13.7% and biaxial loading induces up to a 40% reduction in strength and a 54% decrease in the residual ultimate displacement of the corroded pier. For the same corrosion degree, the dissipated energy under the SS biaxial displacement path is the largest among the four loading paths.

Impact of dynamic strain aging on multiaxial low cycle fatigue behavior of nickel-based alloy 690 at 350 °C

The multiaxial low cycle fatigue behavior of nickel-based alloy 690 at 350 °C was investigated. The multi-slip planar dislocation configuration under non-proportional loading paths is attributed to short-range order (SRO) and dynamic strain aging (DSA). The effect of multiaxial loading paths on DSA is quantitatively evaluated based on average stress drop, which is dominated by axial strain amplitude and weakened by the cross-slip strength. Finally, the preferential oxidation along the slip bands accelerates the nucleation and propagation of microcracks, and the multi-slip cracking for non-proportional loading paths enhances the oxidation damage and further reduces fatigue life.

Evolution law of small strain shear modulus of expansive soil: From a damage perspective

It is of great significance to study the nonlinear evolution law of the small strain shear modulus of expansive soil for analyzing the deformation behavior of soil or geotechnical structure and the seismic site response. Existing studies rarely discuss the damage mechanism of the small strain shear modulus of expansive soil, and the corresponding damage model describing the small strain stiffness decay law is lacking. In this study, a series of resonance column tests were carried out to investigate the effects of mean effective stress, loading and unloading stress paths and vibration cycles on the nonlinear decay law of small strain shear modulus of expansive soil, and the damage mechanism was discussed in detail. Subsequently, a novel damage model describing the decay law of small strain shear modulus of expansive soil was proposed and verified by the results of resonant column tests. The results show that the decay process of the small strain shear modulus with the shear strain is essentially the damage of the soil structure, which can be characterized mathematically by damage model. The mean effective stress and the larger overconsolidation ratio caused by the unloading process can inhibit the damage, while the vibration cycles can cause small reduction in small strain shear modulus and promote the damage. The proposed damage model with clear physical meaning can well describe the evolution law of small strain shear modulus of expansive soil, and has higher accuracy than the traditional model.

The constitutive behavior and dissociation effect of hydrate-bearing sediment within a granular thermodynamic framework

Considering the energy dissipation caused by hydrate dissociation and granular rearrangement at the micro level, a multiphase constitutive model of hydrate-bearing sediment is established within a granular thermodynamic framework. This model incorporates the nonlinear expression of bonding stress into the elastic energy density function, considers the relative velocities of the gas and liquid phases in terms of the solid phase in the dissipative force system, and introduces the coupling effect of heat conduction into the migration coefficient matrix to capture the complex behavior of the sediment. Defining the migration coefficient matrix and elastic energy function, the effective stress is obtained and is suitable for constant hydrate saturation and hydrate dissociation conditions. Dilatancy equations are improved by considering the effect of compactness, bonding stress, and hydrate saturation. Meanwhile, the calculation method of bonding stress is suitable for both strong and weak cementation conditions. The deduced model is validated against the test results conducted on natural and synthetic samples under different hydrate saturations, sediment porosities, and hydrate habits and can effectively capture the strain hardening and softening as well as the dilatancy properties of the sediments and the loading path effect.

Effects of biaxial loading path on seismic behavior of T-shaped RC walls

T-shaped RC walls are commonly used to resist horizontal seismic excitations in multiple directions. The differences in the intensity and spectrum characteristics of two translational components of ground motion cause the wall to experience complex biaxial displacement trajectories, resulting in a different seismic response compared to the behavior derived from conventional uniaxial cyclic tests. Thus, to investigate the seismic behavior and coupling mechanism of T-shaped walls subjected to different magnitudes of loading in two orthogonal directions, this study examined five identical T-shaped walls under uniaxial loading along two principal axes and biaxial loading with three represented loading paths. The test results showed that the mechanical behavior in one direction was significantly affected by the loading in the orthogonal direction owing to internal force redistribution and additional stress caused by the biaxial coupling bending, resulting in vertical variation and intersection of their hysteretic curves. Further, the biaxial loading primarily aggravated the cracking and damage of the flange, which accelerated the performance degradation in the flange direction and reduced the effective flange width involved in resisting web direction load. In addition, the biaxial coupling effect was found to be proportional to the area enclosed by the loading path. Thus, the most severe damage and performance degradation were observed under a square path, followed by an eight-shaped path, with the cruciform path exhibiting the least effect. Consequently, based on the results, recommendations for the design of T-shaped walls subjected to biaxial earthquake actions were proposed.

Effect of Heat Treatment and Loading Path on Non-proportional Fatigue Behavior and Fracture Characteristics of an Al-Si Casting Alloy

Effect of Heat Treatment and Loading Path on Non-proportional Fatigue Behavior and Fracture Characteristics of an Al-Si Casting Alloy

On Dimensional Control in Rotary Stretch Bending of Aluminum Profiles: Loading-Path Effects

In this research, the influences of loading paths on dimensional accuracy in a newly developed flexible rotary stretch bending process were investigated by experimental and numerical approaches. A series of carefully controlled bending experiments were conducted using AA6082-T4 rectangular, hollow profiles. Several representative loading paths — including (i) kinematically-controlled simultaneous stretching and bending; (ii) pre-stretching prior to bending; (iii) post-stretching subsequent to bending; (iv) pre-stretching prior to and post-stretching subsequent to bending — were designed and tested for a given geometrical configuration of bent parts. The critical dimensional characteristics, such as global shape (elastic springback) and cross-sectional deformation, were analyzed and discussed for the products formed under the above-designed loading paths (i)-(iv). Furthermore, finite element analysis was conducted to gain additional insights into the deformation mechanisms that take place for various loading paths. Finally, a guideline for designing the loading paths was developed, thus providing improved process control for achieving formed products with high dimensional accuracy.